I have the answers for a - d, but need e. Weights of female cats of an exotie br

Question

I have the answers for a - d, but need e.

Weights of female cats of an exotie breed are normally distributed with a mean of 4.1 kg and standard deviation of 0.6 kg. a. What proportion of female cats have weights between 3.6 and 4.5 kg? b. What proportion of female cats have weights greater than 1 standard deviation 3) above the mean? How heavy is a cat whose weight is the 80th percentile? A random female cat is selected and weighed. What is the probability that its weight is over 5 kg? Five cats are randomly selected. What is the probability that only one has a weight over 5 kg? c. d. e.

Explanation / Answer

e. Mean is 4.1 and standard deviation is 0.6

P(x>5)=P(z>(5-4.1)/0.6)=P(z>1.5)=1-P(z<1.5), from normal distribution table we get 0.9332

Now, choose 1 out of 5 cats in 5C1 ways. only one has weight over 5kg and rest four have below 5kg thus, answer is 5*(0.9332)*(1-0.9332)^4

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